The Book of Changes clarifies distinctions through diagrams.

予初讀易，惟知朱子《本義》而已。年垂三十，始集漢魏以後諸家傳注，與裡中同志者講習，乃頗涉其津涯。因嘆朱子篤信邵子之過，而《本義》卷首之九圖為可已也。友人德清胡朏明先生，精於明學，庚辰仲夏，示予以《易圖明辨》十卷，則《本義》之九圖咸為駁正，而謂朱子不當冠於篇首。予讀之大喜，躍然曰：至哉言乎，何其先得我心乎！

I used to read the Zhou Changes, knowing only Zhu Xi's The Original Meaning of the Zhou Changes during my early years. When I was about to turn thirty, I began collecting commentaries from the Han and Wei dynasties onwards, and studied with like-minded friends in my hometown. Only then did I begin to understand the entrance to the study of the Zhou Changes. Then I felt that Zhu Xi had placed too much trust in Shao Yong's learning from the Northern Song Dynasty. The nine diagrams listed at the beginning of The Original Meaning of the Zhou Changes are actually entirely unnecessary. My friend, Mr. Hu Wei from Deqing (with the courtesy name Feiming), had a very profound understanding of this subject. In the summer of Gengchen year (the thirty-ninth year of the reign of Emperor Kangxi), he showed me his ten-volume work, The Clear Discrimination of the Diagrams of the Zhou Changes. In this book, he critically examined the nine diagrams at the beginning of The Original Meaning of the Zhou Changes, arguing that Zhu Xi should not have placed them at the beginning of the entire text. After reading this, I was very pleased and jumped up exclaiming: How accurate this is! It seems to have exactly hit what I was thinking.

予嘗謂河圖洛書、先天後天、羲文八卦、六十四卦方圓諸圖，乃邵子一家之學，以此為邵子之易則可，直以此為羲、文之易，則大不可。乃朱子恪遵之，反若羲文作易本此諸圖，不亦異乎？夫河圖見於《顧命》《繫辭》《論語》，古固有之，而後世亡之矣。今之自一至十之圖，本出陳希夷，古人未嘗語及，非真河圖也。戴九履一之圖，今之所謂洛書者，見於《漢書·張衡傳》及緯書《乾鑿度》，乃太乙下行九宮圖，非洛書也。後世術家配以一白二黑之數，至今遵用不變，豈果真洛書乎。

I have always thought that the entire system of diagrams, including the River Chart and the Luo Square, the Earlier Heaven and Later Heaven diagrams, the Eight Trigrams of Fuxi and King Wen, and the sixty-four hexagrams in square and circular forms, are all the contributions of Shao Yong alone. It is acceptable to regard them as part of Shao Yong's study of the I Ching, but to directly consider them as the study of Fuxi and King Wen is most inappropriate. Yet Zhu Xi respectfully followed them, as if Fuxi and King Wen composed the I Ching based on these diagrams, which is very strange. The term "River Chart" appears in the "Book of Documents · Gu Ming," the "Great Treatise" of the I Ching, and the "Analects." In ancient times, there was indeed such a thing, but it has long since been lost. The diagram of black and white dots from one to ten that is currently passed down is actually transmitted by Chen Tuan, a Daoist of the Five Dynasties and early Song Dynasty, who was known as Master Xiyi. Ancient scholars never mentioned it, so it is not the true River Chart. The diagram known as "Daijiu" or "Wearing One on the Sole," which is what modern people call the Luo Square, appears in the "Biography of Zhang Heng" in the "Book of Han" and the esoteric text "Gan Zao Du." Originally, it was a diagram of the "Taiyi moving through the nine palaces," and it is not the true Luo Square. Later numerologists added the numbers of the nine stars, such as one white and two black, and this has been used continuously up to the present day. How can it be the true Luo Square?

卦止有出震齊巽之位，乃孔子之所繫，而文王周公之遺法也，安得有先天之位？此誰言之而誰傳之？「天地定位」一節，不過言八卦之相錯耳，何曾有東西南北之說，而欲以是為先天卦位乎？此不特先天二字可去，即後天二字亦必不可存。蓋卦位止一而無二，不得妄為穿鑿也。八卦之序，自當以父母六子為次，孔子《繫辭》屢言之，乃舍此不遵，以乾兌離震巽坎艮坤為次，此何理乎？

The directional arrangement of the Eight Trigrams is only explained in the "Shuo Gua Zhuan" as "The Emperor emerges from Zhen, and harmonizes with Xun," which is the text transmitted by Confucius, also passed down by King Wen and the Duke of Zhou. How could there be any notion of "Earlier Heaven" direction? Who said this and who passed it down? The section in the "Shuo Gua Zhuan" called "Heaven and Earth are positioned" merely discusses the mutual opposition of the Eight Trigrams and the intermingling of yin and yang. It never mentions the directions of southeast, northwest, etc. How can it be used to confirm the so-called Earlier Heaven positions? In this case, not only should the term "Earlier Heaven" be deleted, but the term "Later Heaven" should also be discarded, because there is only one set of trigram positions, and there is no second set. There should be no arbitrary fabrication. The order of the Eight Trigrams should naturally follow the sequence of Qian and Kun as parents giving birth to the six sons: Zhen, Kan, Gen, Xun, Li, and Dui. Confucius repeatedly mentions this in the "Xi Ci Zhuan." However, nowadays this order is abandoned, and instead the sequence of Qian, Dui, Li, Zhen, Xun, Kan, Gen, and Kun is used. What is the reason for this change?

太極生兩儀、兩儀生四象、四象生八卦，固出於《繫辭》，而實非生卦之謂也。乾坤生六子，其理顯然，而坤可置於最末乎？三男三女，可錯亂而無序乎？易但有三畫之卦，重之則為六畫，未嘗有二畫四畫五畫之卦也；但有八卦六十四卦，未聞八卦重為十六、十六重為三十二、三十二始重為六十四也。必曰一每生二，以次而加，試問易中曾有是說乎？

The saying "The Supreme Ultimate gives rise to the Two Principles, the Two Principles give rise to the Four Images, the Four Images give rise to the Eight Trigrams" is indeed from the Great Treatise, but it does not actually describe the process of generating the trigrams. The trigrams Qian and Kun produce six children, and the reasoning is clear, yet in the Earlier Heaven sequence, why is the trigram Kun placed last? How can the three male and three female trigrams be so disordered with no clear order? The Zhou Changes contains only three-line basic trigrams, and by overlapping them, they form the six-line composite trigrams. There are no two-line, four-line, or five-line trigrams in the Zhou Changes. There are only the Eight Trigrams and the sixty-four trigrams, and there is no mention of the Eight Trigrams first being overlapped to form sixteen, then sixteen overlapping to form thirty-two, and thirty-two overlapping to form sixty-four. If one insists that each generation doubles the number, then please ask, has the Zhou Changes ever mentioned such a concept?

至於卦變，惟程蘇二家為可信，古人十闢之說，予猶不敢從。若朱子之《本義》，益為支離。況與《啟蒙》之言不合，一人而持兩說，令學者何所適從？此予必不敢附會者也。凡此諸說，間與友人言之，或然或不然。讀先生此書，一一為之剖析，洵大暢予懷。而其採集之博，論難之正，即令予再讀書十年，必不能到。何先生之學大而能精如此！以此播於人間，易首之九圖即從此永廢可也。四明同學弟萬斯同纂

As for the concept of "guabian" (changing hexagrams), only Cheng Yi and Su Shi's interpretations are credible; the ancient idea that the ten derived hexagrams generate the miscellaneous hexagrams is something I still dare not follow. For instance, the hexagram changes listed in Zhu Xi's "The Original Meaning of the Zhou Changes" are even more fragmented and inconsistent with his own explanations in "The Awakening of the Study of the Changes." How can a single person hold two contradictory views? What should scholars follow? This is something I certainly dare not fabricate. These views, I have occasionally shared with my friends, and some agree while others do not. After reading Mr. Hu's book, I found that he thoroughly analyzed each issue, which truly made me feel relieved. His extensive collection of materials and precise arguments are so thorough that even if I studied for another ten years, I would not reach such a level. How could Mr. Hu's scholarship be so vast and profound? If this book were to be circulated among people, the nine diagrams at the beginning of the "Zhou Changes" would eventually be discarded forever. Wansong, a fellow student from Mingsheng (Ningbo), compiled this.

古者有書必有圖，圖以佐書之所不能盡也。凡天文、地理、鳥獸、草木、宮室、車旗、服飾、器用、世系位著之類，非圖則無以示隠賾之形，明古今之制，故詩書禮樂春秋皆不可以無圖。唯易則無所用圖，六十四卦二體六爻之畫，即其圖矣。白黑之點、九十之數、方圓之體、復姤之變，何為哉？其卦之次序方位，則乾坤三索、出震齊巽二章盡之矣，圖可也，安得有先天後天之別？

In ancient times, whenever there was a book, there must have been a diagram to supplement what the text could not fully express. For matters such as astronomy, geography, birds and beasts, plants and trees, palaces and houses, chariots and banners, clothing and ornaments, utensils and objects, as well as genealogies and ranks, without diagrams, the hidden and obscure forms could not be shown, and the differences in systems through the ages could not be explained clearly. Therefore, the books of Poetry, Documents, Rites, Music, and Spring and Autumn Annals could not do without diagrams. Only the Zhou Changes (I Ching) did not need diagrams, because the sixty-four hexagrams, with their upper and lower parts and six lines, were themselves the diagrams. As for the black and white dots, the numbers nine and ten, the forms of square and circular diagrams, and the progression from the hexagram Fu to Guo, what are they for? When it comes to the order and position of the hexagrams, the chapters "Three searches of Qian and Kun" and "The Emperor arises from Zhen, harmonizes with Xun" in the Sayings on the Hexagrams have already explained everything thoroughly. According to these, one could draw a diagram, but where would there be a distinction between Earlier Heaven and Later Heaven?

河圖之象自古無傳，從何擬議？洛書之文見於《洪範》，奚闗卦爻？五行九宮初不為易而設，《參同契》先天太極，特借易以明丹道，而後人或指為河圗，或指為洛書，妄矣！妄之中又有妄焉，則劉牧所宗之《龍圖》、蔡元定所宗之《闗子明易》是也，此皆偽書，九十之是非，又何足校乎？故凡為易圖以附益經之所無者，皆可廢也。

The image of the Yellow River Chart has never been passed down since ancient times; how can later generations guess or discuss it? The text of the Luo Writing appears in the "Book of Documents · Hongfan," and how is it related to the hexagrams and lines of the Zhou Changes? The systems of the Five Phases and the Nine Palaces were never originally designed for the Zhou Changes; what Liu Mu refers to as the Earlier Heaven and the Taiji in his "Zhou Yi Cangtongqi" is merely using the Zhou Changes to explain alchemy, yet later people have some claiming it to be the Yellow River Chart and others claiming it to be the Luo Writing, which is truly absurd. Among these absurdities, there is even more absurd: the "Longtu" that Liu Mu takes as his basis and the "Guanziming Yixuan" that Cai Yuanping takes as his basis are all fake books. If this is the case, then whether the Yellow River Chart is nine numbers or ten numbers, and whether the Luo Writing is ten numbers or nine numbers, these distinctions are not worth arguing about. Therefore, all those who add diagrams to the Zhou Changes, using things that are not originally in the classics, can all be discarded.

就邵子四圖論之，則橫圖義不可通，而圓圖別有至理。何則？以其為丹道之所寓也。俞琰曰：先天圖雖易道之緒餘，亦君子養生之切務。人曰丹家之說雖出於易，不過依仿而托之者，初非易之本義，因作《易外別傳》以明之。故吾謂先天之圖與聖人之易，離之則雙美，合之則兩傷。伊川不列於經首，固所以尊聖人，亦所以全陳邵也。觀吾書者，如以為西山之戎首、紫陽之罪人，則五百年來有先我而當之者矣，吾其可末減也夫。康熙丙戌上已，七十四叟東樵胡渭書於顒溪客舍。

Taking Shao Yong's four diagrams into consideration: the horizontal diagram, which presents the order of the Eight Trigrams and the order of the sixty-four Trigrams, does not make sense in terms of meaning. However, the circular diagram has another deeper meaning. Why? Because the circular diagram embodies the principles of alchemy. Yuan dynasty scholar Yu Yan once said: the Earlier Heaven diagram, although merely a continuation of the Way of the Zhou Changes, is also a crucial practice for the cultivation of gentlemen. He also said that the Daoist alchemists' interpretations, although derived from the Zhou Changes, were merely imitations of the Zhou Changes, falsely attributed to them. They were not originally the true meaning of the Zhou Changes, so he wrote "The Transmission Outside the Zhou Changes" to clarify this. Therefore, I believe: the Earlier Heaven diagram and the sage's Zhou Changes, when separated, each has its own beauty, but when combined, they harm each other. Cheng Yi did not include these diagrams at the beginning of the text, not only to honor the sages, but also to protect Chen Tuan and Shao Yong. Those who read this book, if they think I am the one who attacked Cai Yuan Ding (Xishan) and offended Zhu Xi (Ziyang), then five hundred years ago, someone else has already taken on this blame before me, so I may be leniently treated. Written by Hu Wei, an old man of seventy-four, on the Upper Fourth Day of the Third Month in the 45th year of the Kangxi era, at the Yongyang Guest House by the Yongxi Stream.

元幼學易，心疑先後天諸圖之說。庚子得毛西河先生全集中《河圖洛書原舛篇》，讀之豁然，得其原委。友人歙凌次仲廷堪謂元曰：子知西河之辨易，未見德清朏明先生《易圖明辨》，尤詳備也。元識之，求其書不可得。繼在京師見四庫館書目錄之，曰其書一卷辨河圖洛書，二卷辨五行九宮，三卷辨《參同契》先天圖太極圖，四卷辨《龍圖》《易數鉤隱圖》，五卷辨《啟蒙》圖表，六卷七卷辨先天古易，八卷辨後天之學，九卷辨卦變，十卷辨象數流弊，並引據經典，原原本本，於易學深為有功，元鄉注益切。

When I was young and studied the I Ching, I had doubts about the various diagrams of Earlier Heaven and Later Heaven. In the Gengzi year of the Qianlong era (the forty-fifth year), I obtained the complete works of Master Mao Qiling (whose courtesy name was Xihex), particularly the essay "Original Errors of the Yellow River Chart and the Luo Writing," which clarified for me the origins and development of these diagrams. A friend from Xishan, Ling Tingkan (whose name was Cizhong), told me that although I knew Mao Xihex's interpretation of the I Ching, I had not yet seen the work of Master Hu Feiming from Deqing, "Clear Discrimination of the I Ching Diagrams." He said that this book provided especially detailed and comprehensive analysis. I noted his words but could not find the book anywhere. Later, when I saw the catalog of the Four Treasuries Collection in the capital, I recorded its entry, which stated that the book had ten chapters: the first chapter discussed the Yellow River Chart and the Luo Writing, the second the Five Phases and the Nine Palaces, the third the "Threefold Concordance" of the I Ching and the Earlier Heaven Diagram and the Taiji Diagram, the fourth the "Dragon Diagram" and the "Hidden Numbers of the I Ching," the fifth the diagrams in the "I Ching Enlightenment," the sixth and seventh the ancient Earlier Heaven I Ching, the eighth the Later Heaven studies, the ninth the changes of the hexagrams, and the tenth the drawbacks of the use of images and numbers. Everywhere, it cited classical texts and explained the origins and development thoroughly, making a great contribution to the study of the I Ching. My desire to study it became even more intense.

丙辰視學至吳興，始求得讀之，蓋距昔已十六年矣。愧聞道之甚遲，喜斯篇之未泯，亟命其家修板刷印，廣為流傳，以貽學者，因並識其事於篇首。至其圖辨大略，則萬季野先生序言之已盡，茲不贅論。嘉慶元年八月二十八日，浙江督學使者、內閣學士兼禮部侍郎、儀徵後學阮元謹序。

In the third year of the Jiaqing era (the first year of the Jiaqing reign), I, serving as a scholar-official in charge of examinations, arrived at Wuxing and only then obtained this book to read, having heard of it sixteen years earlier. I felt ashamed that I had learned about the Way so late, yet I was delighted that this book had not been lost. I hurriedly instructed the descendants of Hu to repair the old edition and print it again, so that it could be widely circulated and passed on to future scholars. Therefore, I recorded this incident at the beginning of the book. As for the main principles of the book's discussion of diagrams, Mr. Wan Siting (whose courtesy name was Jiyě) has already explained them thoroughly in his preface, so I will not elaborate further. On the 28th day of the eighth lunar month of the first year of Jiaqing, Ruan Yuan, the imperial examiner of Zhejiang, a scholar of the Yizheng school, and a minister of the cabinet and deputy minister of the Ministry of Rites, respectfully presents this preface.

右《易圖明辨》十卷，國朝胡渭撰。按渭原名渭生，字朏明，一字東樵，德清人。事蹟著撰具見江鄭堂《漢學師承記》，稱先生嘗謂：詩書禮春秋皆不可無圖，惟易無所用圖。六十四卦二體六爻之畫即圖也，八卦之次序方位，乾坤三索、出震齊巽二章盡之矣，安得有先後天之別哉？河圖之象自古無傳，何從擬議？洛書之文見於《洪範》，五行九宮初不為易而設，乃作是書云云。

The above is a ten-volume work entitled "Yitu Mingbian" written by Hu Wei of the present dynasty. According to Hu Wei's original name was Weisheng, with the courtesy name Feiming, and also the name Dongqiao, from Deqing, Zhejiang. His life and writings are recorded in Jiang Fan's "Hanxue Shicheng Ji" (Record of the Transmission of Han Learning), where it is stated that Mr. Hu once said: The "Book of Poetry," "Book of Documents," "Book of Rites," and "Spring and Autumn Annals" cannot exist without diagrams, but the "Zhou Yi" (Book of Changes) does not need diagrams. The diagram of the sixty-four hexagrams, with their upper and lower trigrams and six lines, is itself a diagram. The order and direction of the eight trigrams have already been fully explained in the "Shuogua Zhuan" (Commentary on the Trigrams) in the sections "Qian and Kun Three Times" and "The Emperor Emerges from Zhen, Aligns with Xun," so how could there be a distinction between Earlier Heaven and Later Heaven? The image of the River Chart has never been passed down since ancient times, so how can we guess it? The text of the Luo Book appears in the "Shangshu · Hongfan" (Book of Documents · Hongfan). The Five Phases and the Nine Palaces were originally not designed for the "Zhou Yi"—thus he wrote this book, and so on.

又云：洪範古聖所傳，如日月之麗天，有目所共覩，而間有晦盲否塞者，先儒曲說為之害也。漢儒五行傳專主災異，以瞽史矯誣之說，亂彝倫攸敘之經，其害一也；洛書之本文具在《洪範》，宋儒創為黑白之點、方圓之體、九十之位，書也，而變為圖矣，且謂洪範之理通於易，劉牧以九為河圖、十為洛書，蔡元定兩易其名，其害二也；《洪範》原無錯簡，而宋儒任意改竄，移「庶徵王省惟歲」以下為五紀之傳，移「皇斂時五福」至「作汝甲咎」及「三德惟闢作福」以下併為五福六極之傳，其害三也。作《洪範正論》五卷雲雲。其言有足與是書相發明者。

Jiang Fan also recorded that he said: The "Hongfan" (The Mandate of Heaven) was passed down by ancient sages, like the sun and moon hanging in the sky, visible to all who have eyes. Occasionally, there are obscure and difficult-to-understand parts, which are the result of misunderstandings by earlier scholars. The Han dynasty scholars' "Hongfan Wuxing Zhuan" (Commentary on the Five Phases of Hongfan) focused solely on calamities and portents, using superstitious and deceptive language of diviners and historians, which disturbed this classic text that speaks of "the orderly arrangement of the principles of conduct." This is the first kind of harm. The original text of the Luo Book was fully preserved in the "Hongfan," but Song dynasty scholars invented black and white dots, square and circular forms, and the arrangement of numbers nine and ten, turning what was originally a text into a diagram. They also claimed that the principles of the "Hongfan" are connected to the "Zhou Yi" (I Ching). Liu Mu regarded the number nine as the He Tu (Yellow River Chart) and ten as the Luo Shu (Luo Writing), while Cai Yuan Ding reversed the names of the two. This is the second kind of harm. The original "Hongfan" had no misplaced passages, but Song scholars arbitrarily altered and confused the text, moving "Shuying: Wang sheng wei su" and following sections to become the commentary on "Wujì" (Five Celestial Objects), and moving "Huang lian shi wufu" to "Zuo ru jia jiu" and "Sandé: Wei bi zuofu" and following sections to become the commentary on "Wufu Liují" (Five Blessings and Six Curses). This is the third kind of harm. Therefore, he also wrote five volumes of "Hongfan Zhenglun" (Correct Discussion on Hongfan), and so on. These remarks can be very helpful in complementing this book.

先生篤志經學，著述甚夥，所撰《禹貢錐指》一書，曾呈聖祖御覽，賜「耆年篤學」扁，稽古之榮，至今豔稱之。顧四庫提要著錄是書，與阮文達《國朝儒林傳稿》，均稱視《禹貢錐指》尤為有功經學，則其推崇也至矣。咸豐壬子冬至前一日，南海伍崇曜謹跋。

Mr. Hu devoted himself entirely to studying the classics and wrote many works. His book "Yugong Zhenzhi" was presented to Emperor Kangxi for his inspection, and he was awarded a plaque inscribed with "Qinian Duxue" (meaning "advanced age and devoted learning"). This honor of studying ancient texts has been admired by people ever since. Both the "Siku Quanshu Zongmu Tiyao" and the "Guochao Rulin Zhuan Gao" edited by Ruan Yuan (posthumously honored as Wen Da) noted that this book made greater contributions to the study of classics than "Yugong Zhenzhi," indicating the highest level of praise. This inscription was made by Wu Chongyao of Nanhai on the day before the winter solstice of the second year of the Nengzi year of the Xianfeng era.

卷一　河圗洛書。卷二　五行、九宮。卷三　周易參同契、先天太極。卷四　龍圗、易數鉤隠圗。卷五　啟蒙圗書。卷六　先天古易上。卷七　先天古易下。卷八　後天之學。卷九　卦變。卷十　象數流弊。

The entire book consists of ten volumes with the following contents: Volume one discusses the 'Yellow River Chart' and 'Luo Writing'; Volume two discusses the 'Five Phases' and 'Nine Palaces'; Volume three discusses Wei Boyang's 'Zhou Changes Comprehensive Concordance' and the 'Earlier Heaven Diagram' and 'Taiji Diagram'; Volume four discusses the 'Dragon Diagram' and Liu Mu's 'Yi Numbers Hidden Diagram'; Volume five discusses the diagrams and texts recorded in Zhu Xi's 'Yi Learning Enlightenment'; Volume six discusses the upper part of the 'Earlier Heaven Ancient Yi'; Volume seven discusses the lower part of the 'Earlier Heaven Ancient Yi'; Volume eight discusses the 'Later Heaven Studies'; Volume nine discusses the 'Hexagram Transformations'; Volume ten discusses the various evils arising from the transmission of the study of symbolic representations and numbers.

《易圖明辨》十卷，國朝胡渭撰。渭原名渭生，字朏明，號東樵，徳清人。是書專為辨定圖書而作。初，陳摶惟闡易理，衍為諸圖，其圖本凖易而生，故以卦爻反覆研求，無不符合。傳者務神其說，遂歸其圖於伏羲，謂易反由圖而作；又因繫詞河圖洛書之文，取大衍算數作五十五點之圖，以當河圖；取《乾鑿度》太乙九宮法造四十五點之圖，以當洛書。其陰陽竒偶，亦一一與易相應，傳者益神其說，又真以為龍馬神龜之所負，謂伏羲由此而有先天之圖。

The book "Yitu Mingbian" consists of ten volumes and was written by Hu Wei of this dynasty. Originally named Wei Sheng, with the courtesy name Feiming and the style name Dongqiao, Hu was from Deqing, Zhejiang. This book was specifically written to clarify the theories concerning the "Heavenly Chart" and "Luo Writing." Initially, Chen Tuan of the Five Dynasties and early Song Dynasty merely expounded the principles of the "Zhou Changes" and developed them into a series of diagrams; these diagrams were originally derived from the "Zhou Changes," so when comparing the hexagrams and lines repeatedly, they naturally matched. However, those who transmitted the teachings became overly mystical, attributing these diagrams to Fuxi. They claimed that the "Zhou Changes" were actually based on these diagrams. Moreover, since the "Xici Zhuan" mentions "the river produced the chart, the Luo produced the book," they used the large derivation method of divination to create a diagram with fifty-five points, which they used as the "Heavenly Chart." They also took the method of the Taiyi Nine Palaces from the esoteric text "Qian Zao Du" to create a diagram with forty-five points, which they used as the "Luo Writing." The odd and even numbers of points in these diagrams correspond with the "Zhou Changes" in every aspect. The transmitters further exaggerated their significance, even claiming that they were brought forth by the dragon horse and the divine turtle, and that Fuxi thus created the "Earlier Heaven" diagram.

實則唐以前書絶無一字之符驗，而突出於北宋之初。夫測中星而造儀器，以驗中星無不合，然不可謂中星生於儀器也；候交食而作算經，以驗交食無不合，然不可謂交食生於算經也。由邵子以及朱子，亦但取其數之巧合，而未暇究其太古以來從誰授受，故《易學啟蒙》及《易本義》前九圖皆沿其說，同時袁樞、薛季宣皆有異論。

In fact, there is no single character in the classical texts before the Tang dynasty that can confirm these diagrams. Yet they suddenly appeared in the early Song dynasty. For example, instruments were made by observing the position of the central star, and these instruments were used to verify the central star's position without any discrepancy, but one cannot say the central star was created by the instrument. Similarly, calculations were compiled by predicting solar and lunar eclipses, and these calculations were used to verify the eclipses without any discrepancy, but one cannot say the eclipses were created by the calculations. From Shao Yong to Zhu Xi, they only took these diagrams as coincidental in numbers, without investigating who passed them down from ancient times. Therefore, the nine diagrams at the beginning of "Yixue Qimeng" and "Zhouyi Benyi" all followed this tradition. Contemporary scholars of Zhu Xi, such as Yuan Shu and Xue Jixian, proposed different opinions.

然考《宋史·儒林傳》，《易學啟蒙》朱子本屬蔡元定創稿，非所自撰。《晦庵大全集》中載《答劉君房書》曰：啟蒙本欲學者且就大傳所言卦畫蓍數推尋，不須過為浮說。而自今觀之，如河圖洛書，亦不免尚有剰語。至於《本義》卷首九圖，王懋竑《白田雜著》以文集、語類鉤稽參考，多相矛盾，信其為門人所依附，其說尤明。則朱子當日亦未嘗堅主其說也。元陳應潤作《爻變易蘊》，始指先天諸圖為道家假借易理以為修煉之術，呉澄、歸有光諸人亦相繼排擊，各有論述。國朝毛竒齡作《圖書原舛編》，黃宗羲作《易學象數論》，黃宗炎作《圖書辨惑》，爭之尤力。然皆各據所見抵其罅隙，尚未能窮溯本末，一一抉所自來。

But examining the "Biographies of Literati" section in the "Song History," we know that Zhu Xi originally entrusted Cai Yuan ding to draft the book "Yixue Qimeng," and did not himself write it. In the "Wuhu Xiansheng Zhu Wengong Wenji," there is an entry titled "Dapeng Liu Junfang Shu," which says: writing "Yixue Qimeng" was originally intended for scholars to explore the hexagram diagrams and the method of using the yarrow stalks as explained in the "Great Treatise," without making excessive and superficial discussions. Now, looking back, even content related to the Yellow River Chart and the Luo Writing still contains some superfluous remarks. As for the nine diagrams at the beginning of the "Zhouyi Benyi," Wang Maosheng of the Qing dynasty, in his "Baitian Za Zhu," compared Zhu Xi's collected writings with the "Zhu Zi Yulu," and found many contradictions, concluding that these diagrams were later added by Zhu Xi's disciples. This view is especially clear. Thus, Zhu Xi himself did not firmly advocate the theory of the diagrams. In the Yuan dynasty, Chen Yingrun wrote "Yao Bian Yiyun," first pointing out that the diagrams of the Earlier Heaven were fabricated by Daoists to explain alchemical practices through the principles of the I Ching. Wu Cheng and later figures such as Guo Youguang in the Ming dynasty successively criticized and discussed these views. In our dynasty, Mao Qilin wrote "Hetu Luoshu Yuan Chuan Bian," and Huang Zongxi wrote "Yixue Xiangshu Lun," while Huang Zongyan wrote "Tushu Bianhuo," making particularly strong arguments against these theories. However, they only attacked the flaws from their own perspectives, and could not thoroughly trace the origin and development of this theory, revealing the source of each point.

渭此書，卷一辨河圖洛書，卷二辨五行九宮，卷三辨周易參同、先天太極，卷四辨龍圖、易數鉤隠圖，卷五辨啟蒙圖書，卷六卷七辨先天古易，卷八辨後天之學，卷九辨卦變，卷十辨象數流弊，皆引據舊文，互相參證，以箝依託者之口，使學者知圖書之說，雖言之有故、執之成理，乃修煉術數二家旁分易學之支流，而非作易之根柢。視所作《禹貢錐指》，尤為有功於經學矣。

Hu Wei's book is divided into ten volumes. The first volume discusses the Yellow River Chart and the Luo Writing. The second volume examines the Five Phases and the Nine Palaces. The third volume differentiates between the "Threefold Concordance" of the Zhou Changes and the Earlier Heaven Diagram and the Taiji Diagram. The fourth volume distinguishes between the "Dragon Diagram" and Liu Mu's "Diagram of the Hidden Numbers in the Changes." The fifth volume analyzes the diagrams appended to the "Introduction to the Study of the Changes." Volumes six and seven discuss the ancient Changes of the Earlier Heaven. Volume eight examines the Later Heaven studies. Volume nine deals with the changes of the hexagrams. Volume ten addresses the drawbacks of the study of imagery and numbers in the Changes. All these volumes cite existing texts to cross-reference and verify each other, aiming to block the mouths of those who falsely claim to be inspired by ancient sages. This enables scholars to understand that although the theories of diagrams and books may seem to have a historical origin and form a coherent system, they are actually only offshoots of alchemists and numerologists who branched off from the study of the Changes, and not the fundamental basis of the sages in composing the Changes. Compared to his work "Concise Guide to the Yu Gong," this book has made greater contributions to the study of classical texts.

《繫辭傳》曰：古者包犧氏之王天下也，仰則觀象於天，俯則觀法於地，觀鳥獸之文與地之宜，近取諸身，逺取諸物，於是始作八卦，以通神明之德，以類萬物之情。

The *Zhou Yi* *Xi Ci Xia Zhuan* says: In ancient times, when Fu Xi ruled over the world, he looked up to observe the celestial phenomena and looked down to study the principles of the earth. He observed the patterns on birds and animals and the products of the land according to its natural conditions. He took inspiration from the human body nearby and from all things in the world afar. Thus he began to draw the Eight Trigrams, using them to connect with the virtue of the divine and to classify and compare the forms and conditions of all things. Hu Wei placed this passage at the beginning of his entire work precisely to indicate that Fu Xi's creation of the *Yi* was based on observing the heavens and studying the earth, not on the *He Tu* or * Luo Shu*.

朱子曰：俯仰逺近，所取不一，然不過以驗陰陽消息兩端而已。草廬吳氏澄曰：氣之有文者曰象，形之有理者曰法。天有雷風日月，雷風氣也，日月象也，言象可以兼氣；地有水火山澤，水火質也，山澤形也，言形可以兼質。鳥獸之文謂動物，地之宜謂植物。身就人而言，物該服食器用而言。神明，天地之氣象形質，妙而可測、顯而可見者也。德若健順動入陷麗止說，及鼔之散之潤之晅之之屬。萬物，凡動植人器皆是。情，猶言其意義也。

Zhu Xi said: Observing upwards and examining downwards, taking distant and near objects, the objects taken are different, yet they are all used to verify the waxing and waning of yin and yang. Wu Cheng, the master of the Yuan dynasty, said: Among the qi there are those with patterns called 'xiang', and among forms there are those with order called 'fa'. In the sky there are thunder, wind, sun, and moon; thunder and wind belong to qi, while sun and moon belong to xiang. Saying 'xiang' includes qi as well. On the ground there are water, fire, mountains, and marshes; water and fire are substances, while mountains and marshes are forms. Saying 'form' includes substances as well. 'Bird and beast patterns' refer to animals, and 'the suitability of the land' refers to plants. 'Body' refers to human beings themselves, while 'things' include clothing, food, and utensils. 'Shenming' refers to the subtle and inferable principles and the evident and visible aspects of the qi, xiang, form, and substance in heaven and earth. 'De' is like the virtues of the eight trigrams, such as strength, compliance, movement, entering, sinking, adhesion, stopping, and speech, as well as actions such as stirring, spreading, moistening, and scorching. 'All things' include all animals, plants, humans, and objects. 'Qing' is equivalent to the meaning of them.

渭按：易之為書，八卦焉而已。卦各具三畫，上畫為天，下畫為地，中畫為人，三才之道也。羲皇仰觀而得天道，俯觀而得地道，中觀於兩間之萬物而得人道，三才之道黙成於心，故立八卦以象之，因而重之，遂為六十四，所謂兼三才而兩之也。言八卦則六十四卦在其中矣，觀下文所舉離、益、噬嗑等皆因重之卦可知也。夫子言羲皇作易之由，莫備於此。

Hu Wei commented: The book of The Zhou Changes is essentially the Eight Trigrams. Each trigram consists of three lines, with the upper line representing Heaven, the lower line representing Earth, and the middle line representing Humanity. This is the way of the Three Powers of Heaven, Earth, and Humanity. Fuxi observed the celestial phenomena to understand the way of Heaven, examined the geography to understand the way of Earth, and observed the myriad things between Heaven and Earth to understand the way of Humanity. The way of the Three Powers formed silently in his mind, so he established the Eight Trigrams to symbolize it. Then he combined the Eight Trigrams two by two, resulting in the sixty-four trigrams. This is what the "Say of the Trigrams" refers to as "combining the Three Powers and doubling them." When discussing the Eight Trigrams, the sixty-four trigrams are already included within them. Looking at the examples in the "Great Treatise" below, such as the trigrams Li, Yi, and Shihe, which are all examples of creating objects based on observations, they all use combined trigrams, which can be understood clearly. Confucius' explanation of why Fuxi composed the Book of Changes is nowhere more complete than this passage.

河圗洛書乃仰觀俯察中之一事，後世專以圗書為作易之由，非也。河圗之象不傳，故周易古經及註疏未有列圗書於其前者，有之自朱子《本義》始。《易學啟蒙》屬蔡季通起藁（見《宋史·儒林傳》），則又首本圗書，次原卦畫，遂覺易之作全由圗書，而舍圗書無以見易矣。學者溺於所聞，不務觀象玩辭，而唯汲汲於圗書，豈非易道之一厄乎？

The Yellow River Chart and the Luo Writing are merely one aspect of observing the heavens and examining the earth. Later generations mistakenly regarded the charts as the sole reason for Fuxi composing the Zhou Changes, which is incorrect. The image of the Yellow River Chart has not been passed down, so the ancient texts of the Zhou Changes and the commentaries through the ages have never placed the charts before the main text. This practice began only with Zhu Xi's The Original Meaning of the Zhou Changes. The book Yi Xue Qimeng (启蒙 of the Study of Changes) was commissioned by Zhu Xi to be drafted by Cai Yuan ding (whose name was Jitong) (see the Song Shi, the Biography of the Literati). In this book, "The Origin of the Charts" is listed as the first section, and "The Origin of the Hexagrams" follows. This leads people to believe that the origin of the Zhou Changes entirely comes from the charts, and without the charts, the Zhou Changes cannot be understood. Scholars are addicted to the commonly heard views and are unwilling to put in effort to observe the hexagrams and study the line statements. Instead, they rush to pursue the charts. Is this not a calamity for the Way of the Changes?

右論伏羲作易之本不專在圗書。

In the previous section, it was argued that the fundamental basis for Fuxi's creation of the Zhou Changes lies in observing the heavens above and examining the earth below, rather than specifically relying on the Yellow River Chart and the Luo Writing.

天一，地二；天三，地四；天五，地六；天七，地八；天九，地十。

The Great Treatise says: "Heavenly numbers are one, three, five, seven, and nine; earthly numbers are two, four, six, eight, and ten." Among these ten numbers, the odd numbers one, three, five, seven, and nine belong to heaven, while the even numbers two, four, six, eight, and ten belong to earth. The Song dynasty Confucian scholars precisely grasped this passage and regarded it as the Yellow River Chart.

朱子曰：此簡本在第十章之首，程子云宜在此，今從之。此言天地之數，陽奇陰偶，即所謂河圗者也。

Zhu Xi said: This passage originally appeared at the beginning of the tenth chapter of the Upper Great Treatise. Cheng Yi thought it should be moved here, and now we follow Cheng's suggestion. This passage discusses the numbers of heaven and earth, with yang being odd numbers and yin being even numbers, which is referred to as the Yellow River Chart.

天數五，地數五，五位相得而各有合。天數二十有五，地數三十，凡天地之數五十有五，此所以成變化而行鬼神也。（伊川先生曰：變化言功，鬼神言用。白雲郭氏曰：變化見於萬物者也，鬼神運於四時者也。）

The Great Treatise says: Heaven has five numbers, Earth has five numbers. The five positions are paired two by two and each has its union. The total of Heaven's numbers is twenty-five, the total of Earth's numbers is thirty. The combined numbers of Heaven and Earth total fifty-five, which is used to accomplish transformation and the movement of ghosts and spirits. (Cheng Yi said: 'Transformation' refers to the workings of creation and transformation, and 'ghosts and spirits' refer to the functions of creation and transformation. Master Guo Yong said: transformation is manifested in all things, and ghosts and spirits operate within the four seasons.)

朱子曰：此簡本在大衍之後，今案宜在此。

Zhu Xi said: This passage originally appeared after the chapter on "The Great Derivation Number," but now it has been determined to be moved here.

平庵項氏安世曰：姚大老云，「天一地二」至「天九地十」，班固《律歴志》及衛元嵩《元包·運蓍篇》皆在「天數五、地數五」之上。今按新安朱先生《易傳》亦用此說，與「天數五」至「行鬼神也」合為一節，置在大衍之首，今從之。

Ping'an Sir Xiang Anshi said: Yao Dalao (Song dynasty Yao Kuan) mentioned that from "tian yi di er" to "tian jiu di shi" is placed before "tian shu wu, di shu wu" in Ban Gu's "Hanshu · Lüli Zhì" and Wei Yuansong's "Yuanbao · Yunshi pian" from the Northern Zhou dynasty. Now, examining Xin'an Zhu Xi's "Zhouyi Benyi", it also adopts this approach, combining it with "tian shu wu" up to "xing gui shen ye" into one section, placing it at the beginning of the chapter on "dayan zhi shu". Now we also follow this arrangement.

渭按：卦者，易之體，所以立；蓍者，易之用，所以行。韓康伯云：卦，象也；蓍，數也。蓍極數以定象，卦備象以盡數。四語劃然分曉。葢象中雖有數，而終以象為主；數中亦有象，而終以數為主。故夫子言數皆主蓍：曰「極數知來之謂占」，曰「參伍以變，錯綜其數」，曰「極其數遂定天下之象」，曰「幽贊於神明而生蓍，參天兩地而倚數」，曰「數往者順，知來者逆，是故易逆數也」，凡此類無一不以蓍言。

Hu Wei commented: The trigrams are the essence of the Book of Changes, used to establish the principles of images; the divining stalks are the function of the Book of Changes, used to carry out divination. A Jin dynasty scholar named Han Kangbo said: the trigrams belong to "images," and the divining stalks belong to "numbers"; the divining stalks must exhaust numbers in order to determine images, and the trigrams must be complete in images in order to exhaust numbers. These four sentences clearly distinguish the two. Generally speaking, although images contain numbers, they ultimately take images as the main aspect; and although numbers contain images, they ultimately take numbers as the main aspect. Therefore, whenever Confucius spoke about "numbers," he was referring to the method of using the divining stalks: he said, "To know the future by exhausting numbers is called divination," he said, "By combining three and two, numbers change and intermingle," he said, "By exhausting numbers, the images of the world are determined," he said, "To consult the divine and generate the divining stalks, to take heaven as three and earth as two, and rely on numbers," he said, "To follow the past is to follow numbers, to know the future is to reverse numbers, thus the Book of Changes is about reversing numbers." All these statements are about the method of using the divining stalks.

而此章尤為明白，舉天地之數正為大衍之數張本。其曰五位者，即五奇五偶，非指天數之中五。一、三、五、七、九同為奇，二、四、六、八、十同為偶，是謂五位相得；一與二、三與四、五與六、七與八、九與十，一奇一偶兩兩為配，是謂各有合。於五行五方曷與焉？於天地生成曷與焉？於河圗洛書又曷與焉？

This chapter explains this very clearly: listing the numbers of heaven and earth is precisely to set the stage for the following discussion of "the great derivation number." It refers to "five positions" as meaning the five odd numbers and the five even numbers, not the central "five" in the heavenly numbers. One, three, five, seven, and nine are all odd numbers; two, four, six, eight, and ten are all even numbers. This is called "five positions interacting with each other." One pairs with two, three with four, five with six, seven with eight, and nine with ten, with one odd and one even in each pair. This is called "each having a corresponding partner." How does this relate to the Five Phases and the five directions? How does it relate to the so-called "heavenly generation numbers" of "heaven produces and earth forms"? How does it relate to the Yellow River Chart and the Luo Writing?

又按：章中言數者三：一曰天地之數，二曰大衍之數，三曰萬物之數。葢天地之數為大衍之法所自出，而萬物之數乃二篇之策適相當耳，於畫卦全無交涉。使五位相得而各有合，果為伏羲所則河圗之象，夫子何難一言以明之，曰「此河圗也」，而顧廋辭隠語，使天下後世之人百端推測邪？至其後章雖言河圗，而與洛書並舉，且與神物、變化、垂象比類而陳，文勢語脈遙遙隔絶，又安見此河圗者即前五十有五之數邪？

Again, it is noted that in this chapter, the term "number" appears three times: first, the numbers of heaven and earth; second, the numbers of the Great Derivation method; and third, the numbers of all things. The numbers of heaven and earth are the source from which the Great Derivation method originates, while the numbers of all things are merely the fact that the sixty-four hexagrams in the upper and lower chapters correspond exactly in their counts, having nothing to do with drawing the hexagrams. If "the five positions are in harmony and each has its counterpart" is indeed the image of the Yellow River Chart that Fuxi followed, then why is Confucius adding the statement "this is the Yellow River Chart"? What difficulty is there in this? Why would he deliberately use a cryptic expression, causing later generations to make endless guesses? As for the following chapter, although it mentions the Yellow River Chart, it is mentioned alongside the Luo Writing, and is presented in parallel with the statements about "the heavens producing divine objects," "the transformation of heaven and earth," and "the heavens displaying omens." The flow of the text and the connection of the words are far removed from the previous passage. How can we then determine that the Yellow River Chart mentioned here is the same as the one with the number fifty-five?

或問：五位以蓍法言之，其相得有合之實，亦有可見者乎？曰：有。一變所餘之策，左一則右必三，左二則右亦二，左三則右必一，左四則右亦四，非奇與奇相得、偶與偶相得乎？二變三變所餘之策，左一則右必二，左二則右必一，左三則右必四，左四則右必三，非一奇一偶兩兩為配而各有合乎？若夫一六、二七、三八、四九、五十之相合，而為天地生成之數、水火木金之象，此後世五行家言，豈易之所有哉？

Someone asked: When referring to the concept of "five positions," if we consider the method of divining with yarrow stalks, is there a visible manifestation of "mutual compatibility" and "mutual pairing"? The answer is yes. In the first change, the remaining number of stalks in the left hand, if one remains, the right hand must have three left; if two remain, the right hand also has two left; if three remain, the right hand must have one left; if four remain, the right hand also has four left. This is not precisely the mutual pairing of odd numbers with odd numbers and even numbers with even numbers, known as "mutual compatibility"? In the second and third changes, the remaining numbers of stalks in the left hand, if one remains, the right hand must have two left; if two remain, the right hand must have one left; if three remain, the right hand must have four left; if four remain, the right hand must have three left. This is not precisely the pairing of one odd and one even, forming pairs, known as "mutual pairing"? As for pairing one with six, two with seven, three with eight, four with nine, and five with ten, and interpreting them as the numbers of heaven and earth generating the world, and the images of water, fire, wood, and metal, this is the interpretation of later Five Phases scholars. The Zhou Changes does not contain such things.

右論天地之數不得為河圗。

The above section argues that the numbers of heaven and earth discussed in the Great Treatise cannot be regarded as the Yellow River Chart.

大衍之數五十，其用四十有九。（兼山郭氏曰：凡數有母、有法、有實。蓍之母，四十九是也；蓍之法，四是也；蓍之實，三十六、二十四、二十八、三十二是也。數有是母，必有法以用之，然後得是實，三者闕一，則蓍道絶矣，此聖人幽贊神明之道也。白雲郭氏曰：是三者之數，莫知所立之後先。謂四十九為先乎，則非法之四，亦不用四十九矣；謂法之四為先乎，則非三十六、二十四、二十八、三十二，亦不用法之四矣。故三者之數，一有一無則蓍之道不立，一先一後則蓍之用不成，惟同冇同立，莫知先後，故其數一本於自然，如環之無端，雖聖人不能加毫末於是矣。）

The Great Treatise of the Upper Classic says: The number of the Great Derivation is fifty, but only forty-nine is actually used. (Master Jiusan Guo Zhongxiao said: All numbers have a "mother," a "method," and a "realization." The mother of the divination method with the yarrow stalks is forty-nine; the method is four; and the realization consists of the numbers thirty-six, twenty-four, twenty-eight, and thirty-two, which are the numbers obtained through the process of counting the stalks. With the mother, one must use the method to apply it, and only then can the realizations be obtained. If any of these three is missing, the way of divination with yarrow stalks is cut off. This is precisely the reason why the sage secretly supports the divine. Master Baiyun Guo Yong said: The numbers of these three elements cannot be known which comes first or which comes later. If one says forty-nine comes first, but without the method of four, forty-nine cannot be used. If one says the method of four comes first, but without the realizations of thirty-six, twenty-four, twenty-eight, and thirty-two, the method of four has nowhere to be applied. Therefore, if one of these three is present and the other is absent, the way of divination with yarrow stalks cannot be established. If one comes first and the other comes later, the function of divination cannot be realized. Only when all three are present at the same time and established together, without distinguishing order, can the numbers be entirely based on nature, like a circular ring with no beginning or end. Even the sage cannot add or subtract anything in this regard.)

分而為二以象兩，掛一以象三，揲之以四以象四時，歸奇於扐以象閏，五歲再閏，故再扐而後掛。（朱子曰：兩，謂天地也。掛，懸其一於左手小指之間也。三，三才也。揲，間而數之也。奇，所揲四數之餘也。扐，勒於左手中三指之兩間也。閏，積月之餘日而成月者也。五歲之間，再積日而再成月，故五歲中凡有再閏，然後別起積分；如一掛之後，左右各一揲而一扐，故五者之中凡冇再扐，然後別起一掛也。又曰：掛一歲，右揲二歲，扐三歲，一閏也；左揲四歲，扐五歲，再閔也。）

The Great Treatise says: divide the yarrow stalks into two parts to symbolize the two principles of heaven and earth; take one stalk to hold between the fingers to symbolize the three elements of heaven, earth, and humanity; count the stalks in groups of four to symbolize the four seasons; place the remaining stalks between the fingers to symbolize the leap month; there are two leap months in five years, so after two times of handling and placing the remaining stalks, one should again hang a stalk. Zhu Xi explains: 'two' refers to heaven and earth; 'hang' means to suspend one stalk between the index finger and the little finger of the left hand; 'three' refers to the three elements; 'discern' means to count in groups; 'odd' refers to the remaining stalks after counting in groups of four; 'place' means to hold the remaining stalks between the fingers of the left hand; 'leap' refers to accumulating the extra days of each month into a month. In five years, two such accumulations form a leap month, so there are two leap months in five years, and then a new cycle begins; just as after hanging one stalk, one discerns and places on both sides, so there are two times of placing in the five steps, and then a new hanging begins. Zhu Xi also says: hanging one stalk corresponds to the first year, discerning on the right corresponds to the second year, placing corresponds to the third year, which is the first leap; discerning on the left corresponds to the fourth year, placing corresponds to the fifth year, which is the second leap.

乾之策二百一十有六，坤之策百四十有四。（韓氏曰：陽爻六，一爻三十六策，六爻二百一十六策；陰爻六，一爻二十四策，六爻百四十四策。白雲郭氏曰：九六，天地之數也，乾坤之策也；七八出於九六者也，六子之策也，乾坤相索而成者也。）凡三百有六十，當期之日。（朱子曰：少陰退而未極乎虛，少陽進而未極乎盈，故此獨以老陽老陰計乾坤六爻之策數，餘可推而知也。期，周一歲也，凡三百六十五日四分日之一，此特舉成數而槩言之耳。）

The Great Treatise says: The number of strategies for the Qian hexagram is 216, and for the Kun hexagram is 144. Han Kangbo said: Qian has six yang lines, each line has 36 strategies, so six lines total 216 strategies; Kun has six yin lines, each line has 24 strategies, so six lines total 144 strategies. Bai Yun Guo Yong said: Nine and six are the numbers of heaven and earth, which are the numbers of strategies for the Qian and Kun hexagrams; seven and eight are derived from nine and six, which are the numbers of strategies for the six subsidiary hexagrams, generated by mutual inquiry between Qian and Kun. Together, they total 360, which exactly corresponds to the number of days in a year. Zhu Xi said: The lesser yin is retreating but has not yet reached the extreme emptiness, and the lesser yang is advancing but has not yet reached the extreme fullness, so here only the old yang and old yin are used to calculate the six lines of Qian and Kun. The rest can be inferred accordingly. "Period" refers to a whole year, which is actually 365 and 1/4 days. Here it is just a rough approximation using an integer.

二篇之策，萬有一千五百二十，當萬物之數也。（二篇謂上下經。凡陽爻百九十二，得六千九百一十二策；陰爻百九十二，得四千六百八策，合之得此數。）是故四營而成易，十有八變而成卦。（四營謂分二、掛一、揲四、歸奇也。易，變易也，謂一變也。三變成爻，十八變則成六爻也。）八卦而小成。（謂九變而成三畫，得內卦也。）引而伸之，觸類而長之，天下之能事畢矣。（引伸觸類，謂已成六爻而視其爻之變與不變以為動靜，則一卦可變而為六十四卦，以定吉凶，凡四千九十六卦也。）

The Great Treatise of the Upper Transmission says: The total number of divination sticks used in the upper and lower parts is eleven thousand five hundred and twenty, exactly corresponding to the number of all things. (The term 'two chapters' refers to the upper and lower sections of The Zhou Changes. All the yang lines total one hundred and ninety-two, which equals six thousand nine hundred and twelve sticks; all the yin lines total one hundred and ninety-two, which equals four thousand six hundred and eight sticks. Adding these two numbers together gives the total number mentioned.) Therefore, after four steps of divination, one change is completed; after eighteen changes, one hexagram is formed. (The four steps refer to dividing into two, hanging one, counting by fours, and placing the remaining sticks in the palm. 'Change' (yi) refers to one change. Three changes form one line, so eighteen changes form six lines.) The eight trigrams form a small completion. (This refers to nine changes producing three lines, forming the inner trigram.) By extending and applying this principle widely, all things that can be done in the world are fully covered. (Extending and applying this principle refers to after the six lines are formed, determining whether each line changes or remains the same to judge its movement or stillness. Thus, one hexagram can transform into sixty-four hexagrams, used to determine fortune and misfortune, totaling four thousand and nine十六 hexagrams.)

朱子曰：大衍之數五十，葢以河圗中宮天五乘地十而得之。至用以筮，則又止用四十有九，葢皆出於理勢之自然，而非人之知力所能損益也。

Zhu Xi said: The number of great transformation is fifty, which is roughly obtained by multiplying the five heavenly numbers from the Yellow River Chart with the ten earthly numbers. However, when actually used for divination, only forty-nine are used. This is all due to the natural course of things and circumstances, and not something that human intelligence can add to or subtract from.

按：大衍之解，康節云：五者，蓍之小衍也，故五十為大衍。漢上云：小衍之五，參兩也；大衍之五十，則小衍在其中矣。此說近是。五十非以河圗中宮天五乘地十而得之，葢古之立數者，凡畸零不用，故於五十五數去其五，亦猶期三百六十五日四分日之一，而去其畸零以為三百有六十也。且蓍草之生，一本百莖，中分之得五十，彼此參會，皆由自然。

Hu Wei remarked: Regarding the explanation of "da yan zhi shu" (the great derivation number), Shao Yong (posthumous name Kangjie) said: "Wu" (five) is the "xiao yan" (small derivation) of the number of the yarrow stalks, so fifty is called "da yan" (great derivation). Zhu Zhen, the master from Han Shang, said: the "five" of "xiao yan" is the number of heaven and earth, taking two from heaven and two from earth. The "fifty" of "da yan" already includes the "xiao yan." This explanation is closer to the truth. Fifty is not obtained by multiplying the heavenly five of the river chart's central palace with the earthly ten. Instead, in ancient numbering, any remainder was discarded, so five was subtracted from fifty-five. Just as a year actually consists of three hundred sixty-five and one fourth of a day, the ancients discarded the remainder and only took three hundred sixty. Moreover, the growth of the yarrow stalks, one root producing one hundred stalks, when divided exactly gives fifty. The two sides correspond and verify each other, all arising naturally.

及其用也，則又止四十有九。王弼云一不用以象太極，妄也，諸家穿鑿附會尤無理。唯鄭康成云：以五十之數，不可以為七八九六卜筮之占，更減其一，故四十有九。是為正義，而李泰伯、郭子和宗之。

In actual use, only forty-nine strands are used. Wang Bi said that the one strand not used was to symbolize the Taiji, which is a baseless claim; the elaborate interpretations of other schools are even more unreasonable. Only Zheng Xuan said: the number fifty cannot derive the numbers seven, eight, nine, and six, which are used in divination, so one strand is subtracted to make forty-nine. This is the correct explanation. Song dynasty scholars Li Gou (style name Taibo) and Guo Yong (style name Zihe) both followed this view.

（子和曰：世俗皆以三多三少定卦象，如是則不必四十九數，以四十五、四十一皆初揲非五則九，再揲三揲非四則八矣，豈獨四十五、四十一為然哉？自三十以上論之，則三十三、三十七、五十三、五十七、六十一、六十五、六十九、七十三、七十七、八十一、八十五、八十九、九十三、九十七，皆可得五九四八多少之象，與四十九數為母者無以異，獨不可得三十六、二十四、二十八、三十二之策數，故蓍數四十九為不可易之道，可易者非聖人之法也。）此正所謂出於理勢之自然，而非人之智力所能損益者，又何必以河圗太極之五一為蓍法之所自出乎？

Guo Yong said: The common practice is to use the "three more, three less" method to determine the hexagram. If we follow this method, it is not necessarily required to use forty-nine stalks. One could use forty-five or forty-one stalks, and the remainder of the first change would be either five or nine, while the remainders of the second and third changes would be either four or eight. Moreover, why only forty-five and forty-one? Starting from thirty upwards, numbers such as thirty-three, thirty-seven, fifty-three, fifty-seven, sixty-one, sixty-five, sixty-nine, seventy-three, seventy-seven, eighty-one, eighty-five, eighty-nine, ninety-three, and ninety-seven can also produce remainders of five, nine, four, and eight, which are similar to those obtained using forty-nine stalks. Therefore, using forty-nine stalks as the base number is not fundamentally different. The only numbers that cannot be obtained are thirty-six, twenty-four, twenty-eight, and thirty-two, which are the excess numbers in the divination process. Hence, using forty-nine stalks is an unchangeable method, for anything that can be changed is not the method of the sage. This is precisely what is meant by something arising naturally from the circumstances and principles, not something that can be altered by human intellect. Then why must we necessarily regard the number 'five' from the Yellow River Chart's Central Palace and the number 'one' from the Taiji as the origin of the divination method?

蕭山毛太史奇齡《河洛原舛編》曰：間嘗學易淮西，見鄭康成所注太衍之數，起而曰：此非河圗乎？則又思曰：焉有康成所注圗，而漢代迄今不一引之為據者？則又思大衍所注見於李民《易解》者，干寶、崔憬言人人殊，何以皆並無河圗之言？則又思康成所注大傳，其於「河出圗」句既有成注，何以翻引入春秋緯文（河圗九篇，洛書六篇），而不實指之為大衍之數？於是怳然曰：圗哉圗哉，吾今而知圗之所來矣。摶之所為圗，即大衍之所為注也。

Xiao Shan Mao Qilin, a historian, wrote in his work "Original Compilation of Errors in the River Chart and the Luo Writing" that when I was studying the I Ching in the western part of Huai River region, I saw Zheng Xuan's commentary on the Great Derivation Number, and I jumped up saying: "This is not the River Chart?" Then I thought again: How could there be a chart commented on by Zheng Xuan from the Han dynasty to the present day, yet no one has ever cited it as a reference? Then I thought again: Zheng Xuan's commentary on the Great Derivation Number is preserved in Li Dingzuo's "Collected Explanations of the Zhou Changes," and in the same book, the interpretations of Gan Bao and Cui Jing are all different, yet no one has mentioned the River Chart. Then I thought again: Zheng Xuan commented on the "Great Treatise" passage about "the River produced the Chart," and since there was already a commentary available, why did he instead introduce the text from the "Spring and Autumn Writings" saying that the River Chart has nine chapters and the Luo Writing has six chapters, without clearly identifying it as the Great Derivation Number? Then I suddenly realized: Chart, chart, today I have finally understood where the chart comes from! The chart created by Chen Tuan is actually the commentary that Zheng Xuan gave to the Great Derivation Number.

然而大衍之注之斷非河圗者，則以河圗之注之別有在也。大衍之注曰：天地之數五十有五，天一生水在北，地二生火在南，天三生木在東，地四生金在西，天五生土在中。然而陽無耦，陰無妃，未相成也，於是地六成水於北，與天一併（一六在北）；天七成火於南，與地二並（二七在南）；地八成木於東，與天三並（三八在東）；天九成金於西，與地四並（四九在西）；地十成土於中，與天五並（五十在中），而大衍之數成焉。

However, Zheng Xuan's commentary on the "Da Yan" is certainly not the "Heavenly River Chart," because he has another interpretation of "Heavenly River Chart." He explains the "Da Yan" as follows: the numbers of heaven and earth total fifty-five. Heaven begins with one and produces water, located in the north; Earth begins with two and produces fire, located in the south; Heaven begins with three and produces wood, located in the east; Earth begins with four and produces metal, located in the west; Heaven begins with five and produces earth, located in the center. However, the yang numbers have no counterparts, and the yin numbers have no matches, so they cannot be paired to achieve completeness. Therefore, Earth six completes water in the north, paired with Heaven one (one and six reside in the north); Heaven seven completes fire in the south, paired with Earth two (two and seven reside in the south); Earth eight completes wood in the east, paired with Heaven three (three and eight reside in the east); Heaven nine completes metal in the west, paired with Earth four (four and nine reside in the west); Earth ten completes earth in the center, paired with Heaven five (five and ten reside in the center). In this way, the numbers of Da Yan are completed.

則此所為注，非即摶之所為圗乎？康成但有注而無圗，而摶竊之以為圗；康成之注即可圗，亦非河圗，而摶竊之以為河圗。其根其柢，其曲其裡，明白顯著，可謂極快。然而趙宋元明千年長夜，而及今而始得之，其說有二：

Then Zheng Xuan's annotation is precisely the same as the diagram drawn by Chen Tuan. Zheng Xuan only provided the annotation but not the diagram, while Chen Tuan stole it and turned it into a diagram. Even if Zheng Xuan's annotation could be turned into a diagram, it would not be the Yellow River Chart, yet Chen Tuan stole it and falsely claimed it as the Yellow River Chart. The fundamental nature and internal and external intricacies of this diagram are now clearly revealed, which can be called a most satisfying revelation. However, through the thousand-year darkness of the Song, Yuan, and Ming dynasties, it was not until today that this was uncovered. The reasons for this are two-fold:

一則世之言河圗者亦皆知大衍之數，然第以為河圗之陽二十五點、河圗之陰三十點，與大衍之數一三五七九、二四六八十共成五十有五者，其數相合已耳。而其天生地成、地生天成，或北或南，為水為火，能方能圎，有單有復，按之可為形，指之可為象，則河圗有之，大衍不得而有之也。而孰知大衍之數其為形為象原自如此，而人初不知，其長夜一。

First, people who talk about the Yellow River Chart all know the number of the great derivation, but they think that the Yellow River Chart has twenty-five yang points and thirty yin points, which together with the numbers one, three, five, seven, nine, and two, four, six, eight, ten in the great derivation number add up to fifty-five, and this is merely a numerical coincidence. As for the idea that 'heaven is born and earth is formed, earth is born and heaven is formed,' or that they are located in the north or the south, representing water or fire, which can be arranged in a square or a circle, with single and double forms, and through which one can see the shape and the numbers and the symbolic meanings—these are features unique to the Yellow River Chart, which the great derivation number cannot have. Who would have thought that the great derivation number originally possesses such forms and symbolic representations, yet people were completely unaware of them at first? This is the first long night.

一則魏晉以後俗尚王學（謂王弼），而鄭學稍廢，其所遺注第散見於易、詩、書、三禮、春秋疏義及釋文、漢書、文選諸所引注，而迄無成書。故唐惟李鼎祚略採其注於《易解》中，而其在他書，則惟王氏應麟復為彚輯而補於其後。此在劉、邵言易時皆未之見，今摶得其說而不言所自，或亦轉得之他人，而並其所自而亦不之知，皆未可定，則冥冥矣，其長夜二。

Second, after the Wei and Jin dynasties, the scholarly trend favored Wang Bi's interpretations, and Zheng Xuan's studies gradually fell into neglect. His remaining annotations were only sporadically found in the commentaries on the Book of Changes, the Book of Poetry, the Book of Documents, the three Rituals, the Spring and Autumn Annals, as well as in the Classic Interpretations, the annotations to the Han Shu, and the annotations to the Wen Xuan. They were never compiled into a complete work. Therefore, during the Tang dynasty, only Li Dingzuo slightly included Zheng Xuan's annotations in his Collected Explanations of the Zhou Changes. As for those scattered in other texts, only Wang Yinglin of the Song dynasty recompiled them and appended them to the end of the books. These materials were not known to Liu Mu and Shao Yong when they discussed the Book of Changes. Now Chen Tuan has obtained Zheng Xuan's views but does not cite the source; perhaps he obtained them from others, and even the origin is unclear. All these cannot be determined, leaving only confusion. This is the second long night.

乃幸而得白，顯有從來，但當名之為大衍圗，非然則名天地生成圗，非然則名五行生成圗，而斷斷不得名之為河圗。浸假河圗即此圗，則此圗固康成所注者也，其於大傳「河出圗」下，何難直注之曰：所謂河圗，即揲蓍所稱大衍之數，天一地二、天三地四、天五地六、天七地八、天九地十者？而乃又曰：河龍圗發，其書九篇。則豈非衍數河圗截然兩分，數不得為圗，衍不得為畫乎？

Now that the truth has been revealed, the origin is clear: this diagram should be called the "Great Derivation Diagram," or alternatively the "Heaven and Earth Generating Diagram," or the "Five Phases Generating Diagram." It must not be called the "Yellow River Chart." Even if we suppose that the Yellow River Chart is indeed this diagram, then this diagram was originally explained by Zheng Xuan. He directly noted under the phrase "the river produced the chart" in the "Great Treatise" that "the so-called Yellow River Chart is the great derivation numbers used in divination with yarrow stalks, namely, heavenly one and earthly two, heavenly three and earthly four, heavenly five and earthly six, heavenly seven and earthly eight, heavenly nine and earthly ten." What difficulty is there in that? Yet he deliberately added another note saying "the dragon chart appeared in the river, consisting of nine chapters." This clearly shows that the great derivation numbers and the Yellow River Chart are entirely separate matters: numbers cannot be regarded as diagrams, and the derivation numbers from yarrow stalks cannot be regarded as hexagram figures.

《原舛》云數不得為圗、衍不得為畫二句，真千古格言，顧其說猶有不盡然者，餘不可以無辨。謹案：大衍者，揲蓍求卦之法也，大衍之數出於天地之數，而非即天地之數。葢天地之數，易與範共之，凡天下之言數者未有外於此者也；大衍之數，則唯易有之，範不得而有之也。

Hu Wei said: The two sentences "Numbers cannot be taken as diagrams, and the numbers of divination with yarrow stalks cannot be taken as hexagram figures" in the book "Original Errors of the River and Luo" are truly famous sayings of all time. However, Mao Qiling's view still has some inappropriate aspects, which I cannot help but analyze. It is stated: The method of "Da Yan" is the way of divining hexagrams by using yarrow stalks. The numbers of Da Yan come from the numbers of heaven and earth, but they are not equal to the numbers of heaven and earth. This is because the numbers of heaven and earth are shared by the "Zhou Yi" and the "Shang Shu · Hong Fan", and all numbers discussed in the world do not go beyond this scope; while the numbers of Da Yan exist only in the "Zhou Yi" and are not found in the "Hong Fan".

康成注大衍與四象，皆本漢書五行志。志據劉向父子洪範五行傳以推災異，其所引左氏陳災傳說，葢劉歆取大傳之六七八九十，以續洪範之一二三四五，而為生成妃牡之數，意主洪範，初不為易而設。即其末舉坎離二卦，亦以證水為火牡、火為水妃云爾，終於大衍無涉也。

Zheng Xuan's commentary on the Great Derivation and the Four Images is based on the "Five Phases Chapter" of the "Book of Han." The "Five Phases Chapter" derives its reasoning from the "Huang Fan Five Phases Commentary" by Liu Xiang and his son Liu Xin, which interprets calamities and anomalies. Among the passages cited from the "Zuo Zhuan," the story about the fire in the state of Chen is actually a fabrication by Liu Xin, who connected the sixth, seventh, eighth, ninth, and tenth sections of the "Great Treatise" with the first, second, third, fourth, and fifth sections of the "Huang Fan," to form the so-called generation and mutual generation numbers. His intention was to explain the "Huang Fan," not for the "Zhou Yi." Even though the passage at the end mentions the Kan and Li trigrams, they were only used to demonstrate that water is the male of fire and fire is the female of water. In the end, they have nothing to do with the Great Derivation.

唯律歴志言備數則引易大衍之數五十，言鐘律則引參天兩地而倚數，言歴法則引大衍之數四營之象，而以天地之數終焉。大抵五行主洪範，則附以春秋而不及大衍；律歴主大衍，則附以春秋而不及洪範。考厥源流，區以別矣。

Only the "Lüli Zhì" (Chronology and Music Chapter) of the "Hàn Shū" (Book of Han) cites the "Zhou Yi" (I Ching) when discussing "bèi shù" (complete numbers), quoting "dà yǎn zhī shù wǔ shí" (the great derivation number is fifty). When discussing the tuning of bells, it cites "cān tiān liǎng dì ér yǐ shù" (three heavens and two earths to rely on numbers). When discussing the calendar, it cites "dà yǎn zhī shù sì yíng zhī xiàng" (the great derivation number and the four operations of the compass). Finally, it concludes with the "tiān dì zhī shù" (numbers of heaven and earth). In general, the "Wuxing Zhì" (Five Elements Chapter) mainly relies on the "Hóngfàn" (Huang Fan), with a mention of the "Chūnqiū" (Spring and Autumn Annals) but does not involve the great derivation. The "Lüli Zhì" mainly relies on the great derivation, with a mention of the "Chūnqiū" but does not involve the "Hóngfàn". When examining their origins and boundaries, the distinctions are clearly defined.

故劉說雖未嘗有圗，而圗實在其中，藉令繪以為圗，亦但可名天地生成圗，或五行生成圗，而斷斷不得名之曰大衍圗。何也？蓍無五行，無方位，無生成，無配耦也。今試就筮法而按之，自四營成易以至十八變而成卦，格中之所陳，版上之所畫，孰為天生而地成、地生而天成邪？孰居北而為水、居南而為火邪？方者圎者、單者復者皆安在邪？而《原舛》云大衍之數其形其象原自如此，吾所不解。

Therefore, although Liu Xin's explanation did not draw a diagram, the diagram was already contained within his explanation; even if it were drawn, it could only be called the "Heaven and Earth Generating Diagram" or the "Five Phases Generating Diagram," and could never be called the "Great Derivation Diagram." Why is that? Because the method of using the yarrow stalks does not include the Five Phases, directions, generation, or pairing. Now let us check according to the method of divination: from the four preparations forming one change until eighteen changes form a hexagram, what in the compartments of the stalks or the lines drawn on the board corresponds to "Heaven generates and Earth completes, Earth generates and Heaven completes"? What corresponds to the north being water and the south being fire? Where are the round and square, the single and double? The "Original Errors Collection" claims that the number of the Great Derivation inherently possesses such forms, but I cannot understand this.

若乃竊之為河圗，則固有其形其象矣，生成南北、方圎單復，一一不爽，如宋人之所說矣。幸彼不見鄭注，苟見之，則援以相證，更増一重金湯之固矣。然而天地之數終不得為河圗者，則以大傳無明文，而五十有五但可以生蓍，不可以畫卦也。毛公惟知數不得為圗，而不知大衍之數與天地之數不可混而為一；惟知衍不得為畫，而不知鄭注乃劉氏洪範五行之數，非伏羲大衍四營之數也。長夜始旦，明尚未融，此餘之所以不能無辨也。

As for the case where the diagram was stolen and used as the Yellow River Chart, naturally it would have form and image: generation, north and south, square and circle, single and double, each part precise without error, just as the Song people said. Fortunately, the Song people did not see Zheng Xuan's commentary; if they had, they would have verified it with each other, thus adding another layer of protection to this claim. However, the numbers of heaven and earth cannot be regarded as the Yellow River Chart, because the Great Treatise does not explicitly state it, and the number fifty-five can only be used to deduce the method of divination with yarrow stalks, not to draw the hexagrams. Mao Qiling knew only that "numbers cannot be regarded as diagrams," but did not know that the numbers of Da Yan are not the same as the numbers of heaven and earth; he knew only that "the numbers of Da Yan cannot be regarded as hexagram images," but did not know that Zheng Xuan's commentary is actually the numbers from Liu Xiu's "Huang Fan Wu Xing Zhuan," not the numbers of Fuxi's Da Yan four operations. The long night has just begun to dawn, and the light has not yet penetrated thoroughly, which is why I cannot help but clarify this.

總之康成以九篇為河圗，久已認賊作子，而復據生成配耦之數以注易，遂為偽闗易之嚆矢，此所謂藉寇兵而齎盜糧者也，於摶乎何尤？毛公惡宋太過，故其立言往往刻於宋而寛於漢，夫豈平心之論與？

In summary, Zheng Xuan regarded the nine chapters from the writings of the "Wujing" as the Yellow River Chart, which was already treating the enemy as a son; he also used the numbers of generation and pairing to interpret the Zhou Changes, thus becoming the precursor of the false school of "Guan Lang Yi Zhuan." This is exactly what is meant by lending weapons to the enemy and giving food to thieves. If this is the case, how can we blame Chen Tuan alone? Mao Qilin detested the Song scholars too much, so his arguments are often harsh towards the Song people and lenient towards the Han people. Is this considered a balanced view?

右論五行生成之數非河圗並非大衍。

In the previous section, it was argued that the numbers generating the Five Phases are neither the Yellow River Chart nor the Great Derivation Numbers.

易有太極，是生兩儀，兩儀生四象，四象生八卦，八卦定吉凶，吉凶生大業。

The Great Treatise of the Upper Transmission says: The Book of Changes contains the Taiji, from which the two principles arise, from the two principles the four images arise, from the four images the eight trigrams arise, and the eight trigrams are used to determine fortune and misfortune. Once fortune and misfortune are determined, great undertakings can be accomplished. This passage is the main classical basis for the Song Confucian scholars' establishment of the Earlier Heaven sequence diagram (a doubling method of one producing two, two producing four, four producing eight). Therefore, Hu Wei wanted to specifically clarify its original meaning.

劉氏禹錫《辨易九六論》曰：一行《大衍論》云，三變皆剛，太陽之象；三變皆柔，太陰之象；一剛二柔，少陽之象；一柔二剛，少陰之象。

Tang dynasty scholar Liu Yuxi in his "Discourse on the Six Yin and Six Yang of the Book of Changes" said that Buddhist monk Yixing's "Great Derivation Treatise" explained that when three divination steps using the yarrow stalks result in all yang (odd numbers), it represents the image of the sun; when all are yin (even numbers), it represents the image of the moon; when one is yang and two are yin, it represents the image of the lesser yang; and when one is yin and two are yang, it represents the image of the lesser yin.

東坡蘇氏《易論》曰：老者，陰陽之純也；少者，陰陽之雜而不純者也。陽數皆奇而陰數皆偶，故乾以一為之爻，而坤以二。天下之物以少（上聲）為主，故乾之男皆二陰，而坤之女皆二陽。老陽老陰者，乾坤是也；少陰少陽者，乾坤之子是也。

Su Shi, known as Dongpo, wrote in his "Yi Lun" that "old" represents the purity of yin and yang, while "young" represents the mixture and impurity of yin and yang. The numbers of yang are all odd, and the numbers of yin are all even. Therefore, Qian uses one line as a yao, and Kun uses two lines as a yao. The world's things are governed by the side with fewer numbers, so the three male trigrams born from Qian are each composed of two yin lines and one yang line, and the three female trigrams born from Kun are each composed of two yang lines and one yin line. Old yang and old yin are the two trigrams Qian and Kun; young yin and young yang are the six trigrams born from Qian and Kun.

漢上朱氏曰：乾，老陽也；震坎艮，少陽也；坤，老陰也；巽離兊，少陰也。故四象生八卦。

Han Shang Master Zhu Zhen said: Qian is old yang, Zhen, Kan, and Gen are young yang, Kun is old yin, Xun, Li, and Dui are young yin, so the classic text says "the four images give birth to the eight trigrams."

平庵項氏曰：凡繫辭之稱八卦者，即六十四卦也。八卦更相上下，變為六十四卦，故例以八卦稱之。

Ping'an Xiang Anshi said: All the "Eight Trigrams" mentioned in the Great Treatise refer to the sixty-four hexagrams. The eight trigrams are combined one above the other to form the sixty-four hexagrams, so they are still usually called "Eight Trigrams."

虛齋蔡氏清曰：四象生八卦，此八卦該六十四卦者也，故繼之以八卦定吉凶。

Master Xuzhai Cai Qing said: "The four yin-yang pairs give rise to the Eight Trigrams." The term "Eight Trigrams" here includes all sixty-four trigrams. Therefore, the text immediately follows with "The Eight Trigrams determine fortune and misfortune."